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This paper discusses the maximum likelihood (ML) frequency offset estimation and subsequent correction for a space-time block coded orthogonal frequency division multiplexing (STBC-OFDM) system. Carrier frequency offset in OFDM system destroys the orthogonality between subcarriers resulting in performance deterioration. Also, it considerably reduces the diversity gain for STBC. Accurate frequency offset estimation and subsequent correction will significantly improve the performance of a STBC-OFDM system. This paper proposes an averaging approach for frequency offset estimation. The proposed scheme has been simulated with parameters in conformity with WLAN standards in a Rayleigh fading environment. Simulation results show that after the frequency offset correction, the STBC system may acquire the same level of performance as the system that possesses perfect frequency synchronization.